ACT Math Test Tips and Strategies

1. South Central ACT Strategies and Solutions Seminar ACT Test Tips and Strategies

2. Vertical and Horizontal Alignment

3. Overlap Between Tennessee Math Standards and ACT

4. What Determines Student Success on the ACT Mathematics Subtest? • The ACT College and Career Readiness Standards for mathematics are a combination of skills taught beginning as early as grade 2 and extending through a student’s fourth year high school mathematics course. • In order for a student to attain a 21 or higher, the student needs instruction focused on developing a content-rich, conceptual understanding of mathematics at all grade levels.

5. What Determines Student Success on the ACT Mathematics Subtest? • Students need to develop an understanding of the following: • which math ideas are most important, and why they are important • which ideas are useful in a particular context for problem solving • why and how certain key ideas aid in problem solving, which reminds us of the systematic progression of math • how and why an idea or procedure is mathematically defensible • how to flexibly adapt previous experience to new transfer problems.

6. 24 Math Skills Tested on the ACT Algebra • Operations • Single Variable Equations • Functions • Word Problems • Inequalities • Matrices • Complex Numbers • Systems of equations Numbers • Integers • Rational numbers • Statistics • Probability • Sequences

7. 24 Math Skills Tested on the ACT Coordinate Geometry • Points • Lines • Polynomials • Conic Sections • Reflections Plane Geometry • Lines and Slopes • Triangles • Polygons • Circles Other Topics • Solid Geometry • Trigonometry

8. Algebra • 14 pre-algebra questions based on math terminology (integers, prime numbers, and so on), basic number theory (rules of zero, order of operations and so on), and manipulation of fractions and decimals • 10 elementary algebra questions based on inequalities, linear equations, ratios, percents, and averages • 9 intermediate algebra questions based on exponents, roots, simultaneous equations, and quadratic equations • Total: 33 questions

9. Geometry 14 plane geometry questions based on: • Angles • Lengths • Triangles • Quadrilaterals • Circles • Perimeter • Area • Volume • Total: 23 questions 9 coordinate geometry questions based on: Slope Distance Midpoint Parallel Perpendicular lines Points of intersection Graphing

10. Trigonometry • 4 questions based on: • Basic sine • Cosine • Tangent functions • Trig identities • Graphing • Total: 4 questions

11. ACT Math Formulas • The ACT does not always provide formulas at the beginning of the Math Test. This means you need to memorize relevant formulas, so you can recall them quickly as needed.

12. 16 Most Common ACT Math Formulas 1. Arithmetic mean (average) = Sum of values / Number of values Used to calculate the mean value of a given set of numbers. Ex: (10 + 12 + 14 + 16) / 4 = 13 2. Probability = Target outcomes / Total outcomes Used to calculate the chances of something occurring from a set of possible outcomes.Ex: A jar contains five blue marbles, five red marbles, and ten white marbles. What is the probability of picking a red marble at random? 5 / 20 = .25 or 25%

13. 16 Most Common ACT Math Formulas 3. Quadratic Formula: x = −b ± √b²-4ac/2a Used for determining the x-intercepts of a quadratic (parabolic) equation. Ex: A = 1, B = -4, C = 4 x = -4 ± √4² – 4 (1)(4) / 2(1) x = 4 ± √ 16 – 4(4) / 2 x = 4 ± √16 – 16 / 2 x = 4 ± √ 0 / 2 x = 4 / 2 x = 2

14. 16 Most Common ACT Math Formulas 4. Distance Formula: d=√(x2 – x1)² + (y2 – y1)² Calculate the distance between two points on a coordinate plane. Ex. Find the distance between points (6, 6) and (2, 3) d=√(6 – 2)² + (6 – 3)² d=√(4)² + (3)² d=√16 + 3 d=√25 d = 5

15. 16 Most Common ACT Math Formulas 5. Slope Formula: Slope = y₂ – y₁ /  x₂ – x₁ Calculate the slope (angle) of a line that connects two points on a plane. Ex: Coordinates = (-2, -1) (4, 3) s = 3 – (-1) / 4 – (-2) s = 4 / 6 s = 2 / 3 6. Slope Intercept: y=mx+b Formula the defines a line on a plane, given a known slope and y-intercept. Ex: Slope = 2, Intercept point (0,3) y = 2x+3

16. 16 Most Common ACT Math Formulas 7. Midpoint Formula: (x₁+x₂) / 2, (y₁+y₂) / 2 Calculates the midpoint between to points on a plane. Ex: Find the midpoint between (-1, 2) and (3, -6) (-1 + 3) / 2, (2 + -6) / 2 2 / 2, -4 / 2 Midpoint (1, -2)

17. 16 Most Common ACT Math Formulas 8. Area of Triangle: area = (1/2) (base) (height) Calculate the total area within a triangle based on the lengths of the sides. Ex: Base = 5, Height = 8 a = 1/2 (5)(8) a = 1/2 (40) a = 20 9. Pythagorean Theorem: a²+b²=c² Used to calculate the length of an unknown side of a right triangle, given two sides are known. Ex: a = 3, b = 4 c² = 3² + 4² c² = 9 + 16 c² = 25 c = √25 c = 5

18. 16 Most Common ACT Math Formulas 10. Area of Rectangle: area = length x width Calculates the total area within a rectangle shape. Ex: length = 5, width = 2 a = 5 x 2 a = 10 11. Area of Parallelogram: area = base x height Calculates the total area within a parallelogram. Ex: base = 6, height = 12 a = 6 x 12 a = 72

19. 16 Most Common ACT Math Formulas 12. Area of Circle: π * r² Calculates the total area within a circle. Ex: radius = 4 a = π x 4² a = π x 16 a = 50.24 13. Circumference of Circle: circumference = 2π *  r Calculate the length of the outline of a circle. Ex: radius = 7 c = 2π x 7 c = 43.98

20. 16 Most Common ACT Math Formulas 14. Sine (SOH): Sine = opposite / hypotenuse A trigonometric identity that represents the relative sizes of the sides of a triangle and can be used to calculate unknown sides or angles of the triangle. Ex: opposite = 2.8, hypotenuse = 4.9 s = 2.8 / 4.9 s = 0.57 15. Cosine (CAH): Cosine = adjacent / hypotenuse A trigonometric identity that represents the relative sizes of the sides of a triangle and can be used to calculate unknown sides or angles of the triangle. Ex: adjacent = 11, hypotenuse = 13 c = 11 / 13 c = 0.85

21. 16 Most Common ACT Math Formulas 16. Tangent (TOA): Tangent = opposite / adjacent A trigonometric identity that represents the relative sizes of the sides of a triangle and can be used to calculate unknown sides or angles of the triangle. Ex: opposite = 15, adjacent = 8 t = 15 / 8 t = 1.87 Of course, there 

22. Time Management Strategies

23. #1 Work Questions Out of Order • Spending too much time on the hardest problems means you may rush through the easiest. Instead of working questions in order, ask yourself whether a question is a Do Now, Later, or Never. • NOW: Does a question look okay? Do you know how to do it? Do it now. • LATER: Will this question take a long time to work? Leave it and come back to it later. Circle the question number for easy reference. • NEVER: Know the topics that are your worst, if you do not know where to begin, don’t waste time on those questions. Instead, use more time to answer the Now and Later questions accurately.

24. #2 Choose your “Letter of the Day” • Just because you don’t work a question doesn’t mean you don’t answer  it. • There is no penalty for wrong answers on the ACT, so you should never leave any blanks on your answer sheet. • When you guess on “Never” questions, pick your favorite two-letter combo of answers and stick with it. • For example, always choose A/F or C/H. If you’re consistent, you’re more likely to pick up points.

25. #3 Tackling Word Problems • Word problems look a lot of different ways and test a lot of different math concepts, but if you keep these ACT math tips in mind, you should be able to get started on most word problems. • Know the question. Read the problem all the way through and underline the question. • Let the answers help. Look for clues on how to solve. • Break the problem into bite-sized pieces. Every problem has lots of information: Process each piece one at a time and be careful of tricky phrasing.

26. Tackling Word Problems Example A charity is holding a lottery to raise money. A book of 20 tickets sells for $70.00, and a book of 50 tickets sells for $150.00. How much do you save on each ticket by buying a book of 50 tickets rather than a book of 20 tickets? (A) $0.10 (B) $0.20 (C) $0.25 (D) $0.50 (E) $0.75 If you’re not immediately sure how to proceed, jot down the numbers in an orderly fashion: Book of 50    $150    50 Book of 20    $70    20 When you organize the information in this way, you may see that the next step involves division: Book of 50    $150 ÷ 50 = $3.00 Book of 20    $70 ÷ 20 = $3.50 Buying a book of 50 tickets saves $0.50 per ticket, so the correct answer is Choice (D).

27. #4 Skip the Most Difficult Questions • Skip the Most Difficult Math Questions • There are 60 questions, if you answer at least 40 correct you will receive a score of 26. • The questions at the end of each section are the most difficult. This means that, for instance, in the 20-question Math section, you should completely skip the last 4 questions. Focus the energy you would have spent on those questions on getting the other 16 correct.

28. #5 Know Your Weaknesses • Find Your Math Weaknesses and Drill Them • As you take practice ACT exams, each time you miss a question identify the type of question it is. • When you notice patterns to the questions you miss, you then need to practice the subskill.

29. #6 Understand Your Mistakes • Every mistake you make on a test happens for a reason. If you don't understand exactly WHY you missed that question, you will make that mistake over and over again. • On every practice test or question set that you take, mark every question that you're even 20% unsure about. When you grade the test or quiz, review each question you marked as unsure. • In a notebook, write down the question, why you missed it, and how to avoid repeating that mistake. • Organize questions you miss by subject and sub-topic to help you identify patterns. • Conduct “Flashback” reviews of missed standards in order to get the answer correct the next time.

30. #7 Focus on Most Tested Skills • 24 Math skills are tested, however, some are tested more than others. • Example: Numbers-rational numbers is 56 TIMES more likely to appear than the least common skill (complex numbers).

31. Most Common Math Skills Tested

32. Least Common Math Skills Tested

33. #8 Use the RISC Method on All Questions 1. Read the question 2. Information in the question- consider facts in the question and answer choice options 3. Solve: (4 Methods) -Backsolve -Pick Numbers -Translate Words into Math -Strategically Guess 4. Check to make sure that you answered the specific question that was asked, and plug in your final answer to the formula

34. Backsolve Backsolve to save time on the ACT • You can backsolve when you see integers in the answer choices. Start with answer choice C/H unless the question asks for the smallest or largest value. • Plug in the answers to solve the problem, until you land on the correct solutions.

35. Pick Numbers Pick Numbers to avoid complicated Algebra on the ACT • Skip using involved algebraic equations by picking numbers for variables. Avoid picking 0 or 1 because they have special properties.

36. Translate Words into Math • Translate the words in the question into math so that you can solve more easily. • When you see these words, you should use ADDITION: • Increased by • More than • Combined • Together • Total of • Sum • Plus • Added to

37. Translate Words into Math • When you see these words, use SUBTRACTION • Decreased by • Minus • Less • Difference • Between/of • Less than • Fewer than

38. Translate Words into Math • When you see these words, use MULTIPLICATION • Of • Times • Multiplied by • Product of • Increased/decreased by a factor (this type can involve both addition or subtraction and multiplication!)

39. Translate Words into Math • When you see these words, use DIVISION • Per, a • Out of • Ratio of • Quotient of • Percent (divide by 100)

40. Strategically Guess • Multiple-choice tests offer one great advantage: They provide the correct answer right there on the page! • ACT hides the correct answer behind wrong ones, but when you cross off just one or two wrong answers, the correct answer can become more obvious.

41. #9 Use Charts and Pictures to Answer • Some math problems are difficult to visualize, so sketching out a chart or picture of the given information can help you arrive at the correct answer when taking the math portion of the ACT. Here are some tips to keep in mind: • If you’re a visual person, sketching will help you understand what is being asked. • Your sketch doesn’t have to be perfect. Just seeing how the question looks on paper may help you out. • When you’ve got the beginnings of a sketch, step back from it and decide what kind of problem you’re trying to solve. For example, do you need arithmetic, algebra, or geometry to solve it?

42. #10 Know Number Properties • Recognizing number properties will save you time on test day. Number properties rules include: • Odds and evens • Prime numbers • Order of operations

43. #11 Understand ACT Math Relationships • Know the difference between: • Values • Ratios • Percents The ACT test makers place an importance on being able to move easily between percents, fractions, and decimals.

44. #12 Know Your Triangles • You must know the 30-60-90 and 45-45-90 rules. • The ACT does not provide this information at the beginning of the math section, so be sure to memorize this information ahead of time. • Also look out for Pythagorean triplets (3:4:5 and 5:12:13 and their multiples).

45. #13 Find Common Shapes • Find common shapes on the ACT to help you break complex figures into simple polygons. Look in particular for triangles! • When the ACT does NOT mention “Note: Figure not drawn to scale,” you can use the figure to your advantage!

46. #14 Calculator Tips • Make sure your calculator is allowed on Test Day! • May bring any 4-function, scientific, or graphing calculator as long as all formulas have been removed. • Sharing calculators during the test is not permitted, and the test proctor will not provide a calculator. • Set up the problem on paper first. By doing this, you will prevent confusion and careless errors. • Make sure your calculator has Fresh Batteries!

47. #15 Mark and Come Back • Mark the questions that you skip in your test booklet so that you can come back to them easily. • Also, circle the answers that you choose so that you can check the answer grid against your booklet later on. • When you take practice tests, try to practice bubbling in answers as well so that you can do it quickly and accurately on the real thing.

48. #16 ACT Math Common Mistakes Recognize “Red Flags” • Be on the lookout for common trap answers on the ACT. This includes oddball answers and answers that are too small or too big. Do not Skip Steps • ACT math questions can be very sneaky. Problems can appear at first glance deceptively easy. • ACT questions ask for you to apply basic math knowledge in unique ways and often requires you to run through several steps to get to the correct answer. If you don’t write out these steps, you can easily end up with the wrong answer.  

49. ACT Math Common Mistakes • Not Understanding Functions  • Functions tend to be one of the hardest concepts, if not the hardest concept, for most students. Students are usually less familiar with algebraic and/or trigonometric functions than they are with other math concepts such as fractions and percentages. To master the ACT, you must know your functions.

50. ACT Math Common Mistakes • Solving for the Wrong Value • ACT math questions can be tricky because they ask you to apply basic skills in new ways but also because they sometimes phrase questions in weird, convoluted ways. • Use your skills for converting words to symbols, and write down your steps to help you understand which value to solve for in each question.